a story lives forever
Sign in
Form submission failed!

Stay signed in

Recover your password?
Form submission failed!

Web of Stories Ltd would like to keep you informed about our products and services.

Please tick here if you would like us to keep you informed about our products and services.

I have read and accepted the Terms & Conditions.

Please note: Your email and any private information provided at registration will not be passed on to other individuals or organisations without your specific approval.

Video URL

You must be registered to use this feature. Sign in or register.


Return to iteration in 1977: Hadamard, Poincaré and Kleinian groups


First reading of the work of Fatou and Julia
Benoît Mandelbrot Mathematician
Comments (0) Please sign in or register to add comments
Whatever the case, in '47 my uncle thought of it, not because it was, how to say, intellectually challenging but because it was mathematically difficult, and because Julia and Fatou had stopped at the point and couldn't go any further. He gave me the original reprints of Fatou and Julia to read, and I still own the one of Fatou which was an off-print with renumbered pages, one to whatever, two hundred and seventy-five, a combination of three papers, a little book which is a very valuable item, which Fatou had given to him one time. I don't know what happened to the Julia reprint, so I used the Julia collected works as a reference. For me reading the Fatou-Julia was very easy because in a way I was a trained mathematician - I was so under-trained in terms of going to school, and anyhow the school then was very old-fashioned and Paul Levy was so old-fashioned, and I had been reading Paul Levy, so reading Julia and Fatou was not a pain. For many other people it became very difficult. They wrote beautiful sentences in French, where it was not clear, separate. which were the conditions, which were the conclusions. Sometimes it would say it could not be wrong data - and in fact sometimes the argument would be simple and sometimes very difficult. This was mathematics before the great formalisation of later periods. They also sometimes made mistakes, which were forgiven by their time but not forgiven later in their work. Whatever the case, in 1947 or so I read these papers, I studied them and first of all I did not appreciate the contact with anything physical, which for me was so important, and I did not at all appreciate why these things were particularly interesting. And Julia by that time - Fatou already had been long dead, Julia was still alive, he lived to be very old - was he was very much outside of the great men of the times. He was viewed as being old-fashioned, someone who had done something important in the past but well forgotten. So that's chapter one.

Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance during the Second World War, and is famous for his work on fractal geometry - the maths of the shapes found in nature.

Listeners: Daniel Zajdenweber Bernard Sapoval

Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.

Bernard Sapoval is Research Director at C.N.R.S. Since 1983 his work has focused on the physics of fractals and irregular systems and structures and properties in general. The main themes are the fractal structure of diffusion fronts, the concept of percolation in a gradient, random walks in a probability gradient as a method to calculate the threshold of percolation in two dimensions, the concept of intercalation and invasion noise, observed, for example, in the absorbance of a liquid in a porous substance, prediction of the fractal dimension of certain corrosion figures, the possibility of increasing sharpness in fuzzy images by a numerical analysis using the concept of percolation in a gradient, calculation of the way a fractal model will respond to external stimulus and the correspondence between the electrochemical response of an irregular electrode and the absorbance of a membrane of the same geometry.

Duration: 2 minutes, 24 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008